加权超图的Hodge分解
Hodge Decompositions for Weighted Hypergraphs
摘要：
加权超图是加权单纯复形的推广。近年来，人们对加权单纯复形的加权拉普拉斯算子进行了研究。2016年，作为单纯复形同调的推广，超图的嵌入同调被构造出来。本文将加权单纯复形的加权拉普拉斯算子推广到加权超图。研究了加权超图的加权拉普拉斯算子与加权嵌入同调之间的关系。本文将加权单纯复形的Hodge分解推广到加权超图。此外，作为对Hodge分解的补充，我们给出了加权超图的加权Laplacian的非零特征值的一些结果。
英文摘要：
Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a generalization of the homology of simplicial complexes, the embedded homology of hypergraphs was constructed. In this paper, we generalize the weighted Laplacians of weighted simplicial complexes to weighted hypergraphs. We study the relations between the weighted Laplacians and the weighted embedded homology of weighted hypergraphs. We generalize the Hodge decompositions of weighted simplicial complexes to weighted hypergraphs. Moreover, as a complement for the Hodge decompositions, we give some results for the nonzero eigenvalues of the weighted Laplacians of weighted hypergraphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
